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Global Bounded Solutions for the Keller-Segel Chemotaxis System with Singular Sensitivity
Department of Mathematics and Physics, Faculty of Education, University of Gadarif, Gadarif, Sudan
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, China
- 1 Department of Mathematics and Physics, Faculty of Education, University of Gadarif, Gadarif, Sudan
- 2 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 3 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 4 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 5 College of Mathematics and Statistics, Northwest Normal University, Lanzhou, China
- 6 College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou, China
Applied Mathematics·Volume 11 (2020)·Pages 985–990·Published 30 September 2020·DOI10.4236/am.2020.1110064
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Abstract
In this paper, we consider the Neumann initial-boundary value problem for the Keller-Segel chemotaxis system with singular sensitivity (0.1) is considered in a bounded domain with smooth boundary, Ω ⊂ R n ( n ≥ 1), where d 1 > 0, d 2 > 0 with parameter χ ∈ R. When d 1 = d 2 + χ , satisfying for all initial data 0 ≤ n 0 ∈ C 0 and 0 < v 0 ∈ W 1,∞ (Ω), we prove that the problem possesses a unique global classical solution which is uniformly bounded in Ω × (0, ∞).
KeywordsKeller-Segel SystemChemotaxisGlobal Bounded SolutionSingular Sensitivity
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